Interferometer calibration methods and apparatus

ABSTRACT

A Fabry-Perot (FP) interferometer includes substantially parallel first and second reflecting surfaces spaced apart by an optical gap between the first and second reflecting surfaces. The FP interferometer also has a mechanism for controlling the optical gap. The mechanism includes a plurality of electrostatic control plates. Each electrostatic control plate has a fixed control-plate area. Each control plate is adapted to control the optical gap by application of a control-plate voltage. The control-plate areas are related by integral ratios.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of commonly assigned application Ser.No. 10/897,238, filed Jul. 21, 2004 now U.S. Pat. No. 7,110,122 and theentire disclosure of each of which is incorporated herein by reference.This application is also related to co-pending and commonly assignedapplications: Ser. No. 10/428,261, filed Apr. 30, 2003, Ser. No.10/782,488, filed Feb. 18, 2004, and Ser. No. 10/794,636, filed Mar. 5,2004, the entire disclosure of each of which is incorporated herein byreference.

TECHNICAL FIELD

This invention relates generally to interferometer devices, methods formaking such devices, and more particularly to apparatus and methods forcalibrating such devices.

BACKGROUND

Micro-electromechanical systems (MEMS) are systems which are typicallydeveloped using thin film technology and include both electrical andmicro-mechanical components. MEMS devices are used in a variety ofapplications such as optical display systems, pressure sensors, flowsensors, and charge-control actuators. MEMS devices of some types useelectrostatic force or energy to move or monitor the movement ofmicro-mechanical electrodes, which can store charge. In one type of MEMSdevice, to achieve a desired result, a gap distance between electrodesis controlled by balancing an electrostatic force and a mechanicalrestoring force.

MEMS devices designed to perform optical functions have been developedusing a variety of approaches. According to one approach, a deformabledeflective membrane is positioned over an electrode and iselectrostatically attracted to the electrode. Other approaches use flapsor beams of silicon or aluminum, which form a top conducting layer. Forsuch optical applications, the conducting layer is reflective while thedeflective membrane is deformed using electrostatic force to directlight which is incident upon the conducting layer.

More specifically, MEMS of a type called optical interference devicesproduce colors based on the precise spacing of a pixel plate relative tolower (and possibly upper) plates. This spacing may be the result of abalance of two forces: electro-static attraction based on voltage andcharge on the plates, and a spring constant of one or more “supportstructures” maintaining the position of the pixel plate away from theelectrostatically charged plate. One known approach for controlling thegap distance is to apply a continuous control voltage to the electrodes,where the control voltage is increased to decrease the gap distance, andvice-versa. However, precise gap distance control may be affected byseveral factors, including variations in the operating temperaturesexperienced by the interference device, the voltage applied to theinterference device, material variations between support structures andother system variations.

One known method of calibrating an interferometer device is to useanalog control circuitry to produce a continuously variable voltage,which is applied to the pixel plate and the electrostatically chargedplate of the interferometer device, e.g., a bottom plate. Calibration ofthe applied voltages corresponding to various colors is done using acolor sensor that uses color filters and corresponding photosensors tofind the colors of the reflected light.

BRIEF DESCRIPTION OF THE DRAWINGS

The features and advantages of the disclosure will readily beappreciated by persons skilled in the art from the following detaileddescription when read in conjunction with the drawings, wherein:

FIG. 1 is a schematic side-elevation cross-sectional view of anembodiment of an interferometer device.

FIG. 2 is another schematic side-elevation cross-sectional view of anembodiment of an interferometer device.

FIG. 3 is a top plan view of a portion of an embodiment of aninterferometer device.

FIG. 4 is a schematic side-elevation cross-sectional view of anembodiment of an interferometer device.

FIG. 5 is a top plan view of a portion of an embodiment of aninterferometer device.

FIG. 6 is a schematic side-elevation cross-sectional view of anembodiment of a portion of an interferometer device.

FIG. 7 is a schematic side-elevation cross-sectional view of anembodiment of an interferometer device.

FIG. 8 is a graph showing irradiance detected in an embodiment of amethod for calibrating an interferometer.

FIG. 9 is a flow chart illustrating an embodiment of a method forcalibrating an interferometer.

FIG. 10 is a 1931 CIE chromaticity diagram illustrating exemplaryresults of calibrating an interferometer.

DETAILED DESCRIPTION OF EMBODIMENTS

For clarity of the description, the drawings are not drawn to a uniformscale. In particular, vertical and horizontal scales may differ fromeach other and may vary from one drawing to another. In this regard,directional terminology, such as “top,” “bottom,” “front,” “back,”“leading,” “trailing,” etc., is used with reference to the orientationof the drawing figure(s) being described. Because components of theinvention can be positioned in a number of different orientations, thedirectional terminology is used for purposes of illustration and is inno way limiting. For example, those skilled in the art will recognizethat, in the context of the present invention, an interferometer whose“top reflector” is movable relative to a “bottom reflector” isfunctionally equivalent to another interferometer whose “bottomreflector” is movable relative to a “top reflector.”

One aspect of the invention provides embodiments of a method forcalibrating an interferometer having first and second reflectingsurfaces and an optical gap between them. The method embodiments includesteps of providing an actuator adapted to control the optical gap inresponse to application of an electrical signal, illuminating theinterferometer with a beam of monochromatic light at a firstpredetermined angle of incidence, and detecting light reflected from theinterferometer at a second predetermined angle while varying anelectrical signal applied to the actuator, thereby establishing acalibrated relationship between the applied electrical signal and anoptical path length. Thus, calibration of an interferometer device withsuch an actuator is accomplished by measuring relative changes inreflected light, using a photosensor and a single wavelength of incidentlight.

A specific aspect of the invention provides embodiments of aninterferometer (e.g., a Fabry-Perot interferometer) with electrostaticactuation of the cavity spacing, in which one or both sides of theactuator plates are split. In some of these embodiments, this splittingmay be used to form an integral digital-to-analog converter. This allowsthe voltage of each section on the bottom plate, for example, to beswitched between two predetermined potentials, one of which may be aground condition (0 volts), and one may be a predetermined non-zeropotential, V. If desired, both potentials may be different predeterminednon-zero potentials, V′ and V″.

Another specific aspect of the invention includes embodiments of methodsfor calibration of a split-plate device. In at least one embodiment, thegap distances controlled by voltages applied to the split plate arerelated to each other. Thus, in such embodiments also, the calibrationwith respect to voltage can be accomplished by measuring relativereflection using a photosensor and a single wavelength of light.

Yet another aspect of the invention provides embodiments of a method ofusing an electrostatic actuator for calibrating an interferometer. Otheraspects of the invention include embodiments of interferometer devicesand methods for making such devices.

Various aspects of the invention allow calibration of the cavitydistance of an interferometer such as a Fabry-Perot device in a finelydivided series of steps, without using color filters, multiple colorsources, or color-sensing devices. The calibration may be accomplishedusing a single light source, such as an LED or laser with asubstantially monochromatic (single-wavelength) emission, and using asingle photosensor.

A physical result of applying a single voltage to the actuator of thedevice embodiments described herein is an optical gap size. This opticalgap size depends on various factors such as spring constant of supportstructures, plate thickness, and initial gap. These factors can alsovary due to variations in temperature, humidity, atmospheric pressure,etc. Thus, even if the effects were strictly linear, the slope andoffset of optical gap changes due to switching the voltage on each platewould not be known a priori. Generally, the relationship between opticalgap and applied voltage may not be strictly linear, but non-linearitydoes not prevent accurate calibration of an interferometer by usingmethods of the present invention.

In a particularly convenient and effective embodiment of the invention,an interferometer has actuator plates for electrostatic actuation of theoptical-cavity spacing (optical gap), and one or two sides of theactuator plates are split into two or more segments. This splitting ofactuator plates is used to form an integral digital-to-analog converter.That is, the digital-to-analog converter is formed in situ in theinterferometer. This allows the voltage on each section of the bottomplate, for example, to be switched in a binary manner between 0V, forexample, and a fixed potential relative to the top plate. The plateshave areas related by ratios that are powers of two, i.e., ratios of 1,2, 4, 8, . . . , etc. Permutations of the two binary voltages on eachplate section result in relative plate movement that is controlled in afine series of steps. These steps are obtained by selecting only one ofthe two binary voltages to apply to each section of the actuator plate.Thus, in an exemplary case of an actuator having four plates with arearatios of 8, 4, 2, and 1, and permutations of potentials expressedcorrespondingly as (V₈, V₄, V₂, V₁), there are sixteen permutations ofthe two potentials: viz., (0, 0, 0, 0), (0, 0, 0, V), (0, 0, V, 0), (0,0, V, V), (0, V, 0, 0), (0, V, 0, V), (0, V, V, 0), (0, V, V, V), (V, 0,0, 0), (V, 0, 0, V), (V, 0, V, 0), (V, 0, V, V), (V, V, 0, 0), (V, V, 0,V), (V, V, V, 0), and (V, V, V, V). Each of these permutations providesa distinct optical cavity spacing. As mentioned above, instead of the 0volts and V volts of this example, both potentials may be differentpredetermined non-zero potentials, V′ and V″.

Again, as with a single-plate actuator, calibration of an interferometerdevice with such a split-plate actuator is accomplished by measuringrelative changes in reflected light, using a photosensor and a singlewavelength of incident light. The optical gap distances controlled bythe voltage applied to the split-plate actuator are related to eachother. The voltages on the split-plate segments may be set to a desirednominal setting for the wavelength of interest. Then the plate voltagemay be swept to maximize the irradiance of light reflected onto thephotosensor.

Thus, split-plate interferometer devices have the capability ofaccurately controlling changes in gap size using a single controlvoltage. This action is similar to that of a conventionaldigital-to-analog converter (DAC) dividing down a reference voltage orcurrent normally used by DACs and thus producing a desired fraction ofthe reference current or voltage.

The overall gap voltage can be calibrated by using a single-wavelengthlight source, such as a semiconductor diode laser, and a simplesilicon-diode light sensor. Since the wavelength of such a laser,depending on its own internal cavity length and the type ofsemiconductor used in its manufacture, is typically known to within +/−5nm (nanometers), the known wavelength can be used as a reference withrespect to detection of a peak in irradiance of light reflected towardsthe silicon light sensor from the interferometer.

Referring to the drawings, specific apparatus and method embodimentswill be described in the following detailed description.

FIG. 1 is a side-elevation cross-sectional view of an embodimentschematically illustrating an interferometer device 10 to which thepresent invention is applicable. This embodiment is an example of a typeof interferometer commonly known as a Fabry-Perot interferometer. Theembodiment shown in FIG. 1 has a lower element 20 with a lowerreflecting surface 25 and an upper element 30 with an upper reflectingsurface 35. Upper reflecting surface 35 is only partially reflective,allowing a portion of incident light to be transmitted toward lowerelement 20. Upper element 30 is supported by a supporting structure 40,and in this particular embodiment by a second supporting structure 45.Supporting structures 40 and/or 45 may be flexural supports, forexample. The upper and lower elements 20 and 30 are substantiallyparallel (at least in the absence of an electrical signal to an actuator50) and are spaced apart to form an optical gap 15. The gap dimension 16of optical gap 15 is also shown in FIG. 1.

Actuator 50 provides means for controlling the optical gap 15. Actuator50 may be an electrostatic control plate, for example, responsive to anexternal electrical input such as a control-plate voltage (not shown inFIG. 1). Other alternative actuator means for controlling the opticalgap include magnetic, piezoelectric, thermoelectric, andelectromechanical actuators of various known types, for example. Whileactuator 50 is shown attached to lower element 20 in the embodiment ofFIG. 1, it could alternatively be attached to upper element 30 or beattached to both upper and lower elements.

To use the interferometer, incident light rays 60 are directed towardreflecting surfaces 25 and 35, and reflected light rays 70 appear afterinterference occurring in the interferometer. In FIG. 1, the incidentlight rays 60 are oriented at an incident angle 65 relative to theinterferometer top surface (upper reflecting surface 35). Reflectedlight rays 70 are oriented at an angle 75 to upper reflecting surface35. Similarly, reflected light rays 80 are oriented at angle 75 to lowerreflecting surface 25. It should be noted that the reference from whichangles 65 and 75 are measured in the present specification and drawingsis not the conventional reference normal to the surface, but theinterferometer top surface (upper reflecting surface 35), itself.

Those skilled in the art will recognize that light rays 60 and 80 wouldalso normally be refracted in accordance with Snell's law while passingthrough upper element 30, as its refractive index would normally differfrom that of the ambient medium and/or any medium in optical gap 15,e.g., air. For simplicity of illustration, such refraction is not shownin the drawings.

FIG. 2 is another schematic side-elevation cross-sectional view of asimilar embodiment of an interferometer device, illustrating twodifferent sets of light rays. On the left side of FIG. 2, incident lightrays 60 and reflected light rays 70 and 80 represent monochromatic lightused during calibration of the interferometer, incident at predeterminedincident angle 65 and exiting at predetermined angle 75. On the rightside, incident light rays 90 at angle 95 and reflected light rays 100 atangle 105 show representative light rays during subsequent use of theinterferometer after calibration. As shown in FIG. 2, angles 95 and 105may differ from the predetermined angles 65 and 75 used in calibration.Furthermore, for many applications of interferometer device 10, thelight rays 90 incident during use may be polychromatic, and thereflected light rays 100 may be monochromatic in the sense of having aselected hue or dominant wavelength determined by operation of theinterferometer device. For example, in use, the incident light rays 90may consist of white light, and the reflected light rays 100 may be red,green, or blue light in accordance with input applied to actuator 50.Also, in use of the device, the incident and emergent light raysoriented at angles 90 and 100 respectively may include a range of anglesand may not necessarily be limited to fixed angles.

FIG. 3 is a top plan view of a portion of an embodiment of aninterferometer device made in accordance with the invention, and FIG. 4is a schematic side-elevation cross-sectional view of the sameembodiment. In the embodiment shown in FIGS. 3 and 4, actuator 50includes a number of electrostatic control plates 110, 120, 130, 140,and 150. Each electrostatic control plate has a fixed control-platearea. Each control plate is adapted to control the optical gap byapplication of a separate control-plate voltage, as illustratedhereinbelow. The individual control plates may be substantially coplanarand may be substantially parallel to the first and second reflectingsurfaces of the interferometer, as shown in FIG. 4.

In specific embodiments of such an interferometer that are especiallyuseful, the control-plate areas are related by integral ratios, i.e.,the fixed control-plate area of each control plate is an integralmultiple of a constant. In particular, these integral ratios by whichthe control-plate areas are related may be powers of two, i.e., ratiosof 1, 2, 4, 8, . . . , etc. More generally, for a number N of controlplates having this property, the fixed control-plate areas are relatedby integral ratios of 1, 2, 4, . . . , 2^(N−1). For convenience ofillustration, the control-plate areas shown in FIG. 3, whileillustrating an operable configuration, do not necessarily show ratiosthat are powers of two. This actuator configuration having split controlplates with such ratios forms an integral digital-to-analog converter.Thus, the digital-to-analog converter is formed in situ in theinterferometer. This allows the voltage of each section of actuator 50to be switched in a binary manner between a ground condition (0 V) and asingle predetermined non-zero potential.

Another aspect of the interferometer embodiment of FIGS. 3 and 4 is thatthe electrostatic control plates 110, 120, 130, 140, and 150 arearranged in a nested configuration. Thus, there is an innermost controlplate and an outermost control plate, and each control plate except theoutermost control plate is surrounded by another control plate. Thenested configuration is helpful in preventing instability of the opticalgap setting.

FIG. 5, analogous to FIG. 3, is an alternative top plan view of the sameportion of the embodiment of FIG. 4. As shown in FIG. 5, the nestedarrangement may comprise round control plates. In this configurationthere is a round innermost control plate, and each control plate exceptthe round innermost control plate is annular. Other shapes of controlplates, nested or un-nested, may also be used.

FIG. 6 is a schematic side-elevation cross-sectional view of anembodiment of a top-element portion 30 of an interferometer device. Inthis embodiment, top reflecting surface 35 has a film 250 adapted toenhance its (partial) reflectivity. Film 250 may be a stack of layers,each layer having specific desired optical properties so that the entirestack provides the desired reflectivity. Similarly, a film or stack offilms 260 may provide anti-reflective properties on the bottom side oftop-element 30, e.g., to enhance overall contrast of the interferometerdevice. Top element 30 may also be made with only one of the films 250or 260, if desired, by omitting the other film. Many combinations ofthin films useful for enhancing or suppressing reflectivity of opticalsurfaces are known to those skilled in the art.

FIG. 7 is a schematic side-elevation cross-sectional view of anembodiment showing optical and electrical aspects of an interferometerdevice 10 as used during its calibration. To illustrate these aspects ofcalibration, FIG. 7 shows a device like the embodiment of FIG. 4 withnested split-plate actuator, but various methods of calibrationdescribed hereinbelow may also be applied to other device embodiments.

A source 170 of substantially monochromatic light may be used incalibration of the interferometer, e.g., a diode laser or otherlight-emitting diode (LED) with substantially monochromatic lightoutput. An optical apparatus 190, such as a lens, may be used to directthe monochromatic light in the desired direction of incident light rays60. Another optical apparatus 200, such as another lens, may be used todirect reflected rays 70 toward a photosensor 180 responsive to themonochromatic light, such as a silicon photodiode, providing a signalproportional to irradiance detected from the interferometer. Supportstructures 40 and 45 are electrically grounded in the embodimentillustrated.

Source 170 is controlled by an electrical signal 210. The varioussegments of actuator 50 are driven by individual electrical signals 220,e.g., electrostatic actuator-plate voltages. The electrical outputsignal 230 of photosensor 180 is read during the calibration. Acontroller 240 (which may be a programmable computer, such as ageneral-purpose computer of a conventional type with a memory andsuitable inputs and outputs), may be used to apply signals 210 and 220and to collect, convert analog-to-digital (A-to-D), and store signals230. Controller 240 may be an embedded controller of a conventional typewith an embedded memory, appropriate inputs and outputs, A-to-Dconversion, and suitable programming. FIG. 8, showing irradiancedetected from the interferometer during calibration, is describedhereinbelow in connection with methods of calibrating theinterferometer.

Calibration Method

FIG. 9 is a flow chart illustrating an embodiment of a novel method forcalibrating an interferometer, e.g., a Fabry-Perot interferometer. Themethod is applied to an interferometer having first and secondreflecting surfaces and having an optical gap between them, as describedhereinabove. Various steps of the method are denoted by referencenumerals S10, S20, . . . , S70. Various alternate paths through thismethod are shown by arrows, but the order of steps may be variedsomewhat, and some steps may be performed simultaneously.

The method embodiment of FIG. 9 includes a step S10 of providing anactuator adapted to control the optical gap in response to applicationof an electrical signal. In step S20, the interferometer is illuminatedwith a beam of substantially monochromatic light having a predeterminedwavelength. The beam is oriented at a first predetermined angle ofincidence 65 to the interferometer (i.e., to at least one of the firstand second reflecting surfaces). This step of illuminating theinterferometer may be performed with a laser (such as a solid-statediode laser) having a single predetermined laser wavelength.

It should be noted again that the reference from which angles 65, 75,95, and 105 are measured in the present specification and drawings(e.g., in FIGS. 1 and 2) is not the conventional reference normal to thesurface, but the interferometer top surface 35, itself, or the parallelsurface 25. Those skilled in the art will recognize that this referenceis chosen arbitrarily and that the conventional normal reference may beused, provided that suitable geometric changes are made to the claimsand to formulas used for corrections.

In step S40, light reflected from the interferometer is detected at asecond predetermined angle while varying an electrical signal applied tothe actuator (step S30). The step of detecting light reflected from theinterferometer may be performed with an electronic photosensor, such asilicon photodiode.

Thus, a calibrated relationship is established between the appliedelectrical signal and an optical path length of the interferometer, asexplained in more detail below. The data for this calibratedrelationship is recorded by step S50 of storing the photosensor signalsand by step S60 of storing the corresponding actuator signals or thedigital counts that determine the actuator signals, as described above.The calibrated relationship between the applied electrical signal and anoptical path length of the interferometer may be a non-linearrelationship. The calibrated relationship between the applied electricalsignal and an optical path length of the interferometer is determinedfrom at least one set of values of the applied electrical signal and atleast one corresponding set of values of the photosensor signal, takinginto account the known wavelength of monochromatic light.

When the interferometer is used subsequent to calibration, as describedabove in relation to FIG. 2, the subsequently incident light may have atleast one angle of incidence 90 that differs from the predeterminedangle of incidence 65. In step S70, the calibrated relationship iscorrected, if necessary, for the difference in angles of incidencebetween calibration and use.

In such cases, the calibrated relationship is corrected in accordancewith the formulaL _(eff-use) =L _(eff-cal)(sin A/sin B)where A is the first predetermined angle of incidence 65 (used incalibration), B is the second predetermined angle of incidence 95(occurring in use of the interferometer device), L_(eff-use) is theeffective optical cavity length during use, and L_(eff-cal) is theeffective optical cavity length during calibration. Angles A and B ofthis formula are shown with reference numerals 65 and 95 respectively inFIG. 2. Again, after such corrections of the calibration, the calibratedrelationship between the applied electrical signal and an optical pathlength of the interferometer may be a non-linear relationship.

Another difference mentioned above between conditions during calibrationand conditions during use is that, while monochromatic light is used incalibration, the subsequently incident light during use may bepolychromatic (i.e., not monochromatic). In such cases, the subsequentlyincident polychromatic light is nevertheless subject to the calibratedrelationship between the applied electrical signal and optical pathlength of the interferometer. Although the incident light may bepolychromatic, the light reflected from the interferometer issubstantially monochromatic.

The method of FIG. 9 and its various embodiments may, of course, be usedwith an interferometer having an electrostatic actuator comprising anumber of control plates, each having a fixed control-plate area andeach being adapted to control the optical gap by application of acontrol-plate voltage.

The electronic photosensor used for detecting light reflected from theinterferometer may have an analog output signal, which may be convertedby a digital-to-analog converter to a digital photosensor signal.Selected values of the digital photosensor signal may be stored in amemory. The memory may reside in a controller 240 as described above forcontrolling the applied electrical signal and/or for recordingcalibration results. As implied above, the controller may be a computerprogrammed to perform the calibration of the interferometer.

Thus, another embodiment of a method for calibrating an interferometerincludes steps of providing an actuator adapted to control the opticalgap in response to application of an electrical signal, illuminating theinterferometer with a beam of monochromatic light having a predeterminedwavelength, the beam being oriented at a first predetermined angle ofincidence to at least one of the first and second reflecting surfaces,varying the electrical signal applied to the actuator in a series ofdiscrete steps, while detecting light reflected from the interferometerat a second predetermined angle with a photosensor having an analogphotosensor output, converting the analog photosensor output to adigital photosensor signal, storing a digital value of a digitalphotosensor signal corresponding to each discrete step of the electricalsignal applied to the actuator, and calculating an optical path lengthcorresponding to each discrete step of the applied electrical signal,thereby establishing a calibrated relationship between the appliedelectrical signal and optical path length of the interferometer. Again,the calibrated relationship may be corrected for application tosubsequently incident light having at least one angle of incidencediffering from the first predetermined angle of incidence used duringcalibration.

Another embodiment of a calibration method uses a split-plate actuator.This method includes steps of providing an electrostatic actuator havinga number of control plates (each control plate having a fixedcontrol-plate area and being adapted to control the optical gap byapplication of a control-plate voltage), illuminating the interferometerwith monochromatic light, and detecting light reflected from theinterferometer while selectively applying a fixed voltage to eachcontrol plate, thereby establishing a calibrated relationship betweenthe applied control-plate voltage and an optical path length of theinterferometer. As described above, the control plates may besubstantially coplanar and may be substantially parallel to the firstand second reflecting surfaces of the interferometer.

Another calibration method embodiment that is notably efficient andeffective includes steps of providing an electrostatic actuator having anumber N of control plates, each control plate having a fixedcontrol-plate area and each control plate being adapted to control theoptical gap by application of a control-plate voltage, the N controlplates having fixed control-plate areas related by integral ratios of 1,2, 4, . . . , 2^(N−1), illuminating the interferometer withmonochromatic light, and detecting light reflected from theinterferometer while selectively applying a fixed voltage to eachcontrol plate of the N control plates, thereby establishing a calibratedrelationship between the applied control-plate voltage and an opticalpath length of the interferometer.

In this embodiment, then, the fixed control-plate area of each controlplate is an integral multiple of a constant, and the fixed control-plateareas of the control plates are related to each other by integral ratiosthat are powers of two. For various applications, simple arrangementsmay be used, such as two control plates having fixed control-plate areasrelated by integral ratios of 1 and 2, three control plates having fixedcontrol-plate areas related by integral ratios of 1, 2, and 4, or fourcontrol plates having fixed control-plate areas related by integralratios of 1, 2, 4, and 8. For an example with more finely controlledoptical path lengths, N=6 plates may be used, with integral ratios of 1,2, 4, 8, 16, and 32. For N=8 plates, the ratios are 1, 2, 4, 8, 16, 32,64, and 128. Versions with up to at least 24 plates are practical,providing 24 bits of optical-path-length resolution.

All of the method embodiments may be practiced with an interferometerhaving its control plates disposed in a nested configuration asdescribed above and shown in FIGS. 3 and 5.

FIG. 8 is a graph showing irradiance detected in an embodiment of amethod for calibrating an interferometer, performed in accordance withthe invention. Irradiance detected by photosensor 180 is plottedparallel to vertical axis 310 for various values of a digital countproportional to the optical gap plotted parallel to horizontal axis 320.The plotted curve 300 exhibits discrete steps in irradiance due todiscrete steps in actuator motion produced by an actuator like those ofFIGS. 3, 4, 5, and 7 with an integral digital-to-analog converter (DAC)formed by the control-plate arrangement. The curve has two relativemaxima, 330 and 340 where the optical path lengths for two differentorders of interference correspond to maximum reinforcement between lightwaves reflected from upper and lower reflecting surfaces 25 and 35. Therelative minimum 350 of curve 300 occurs where the corresponding opticalpath length produces maximum cancellation due to interference at an oddintegral number of quarter-wavelengths of the monochromatic light usedin calibration. The corresponding optical path lengths for points 330,340, and 350 are thus determined from the known wavelength of themonochromatic light used in the calibration. As mentioned above,typically this wavelength is known to +/−5 nanometers (nm). Thoseskilled in the art are familiar with calculations to determine opticalpath lengths from suitable irradiance data obtained with a knownwavelength (see, e.g., the textbook by Eugene Hecht “Optics” FourthEdition, Addison-Wesley, San Francisco, Calif., 2002, pp. 421–425).

FIG. 10 is a 1931 CIE chromaticity diagram illustrating exemplaryresults of calibrating an interferometer by embodiments of methodsperformed in accordance with the invention. For comparison, triangle 400is shown enclosing chromaticity values from a conventional cathode raytube RGB display. Dashed curve 380 (first order) and solid curve 390(second order) trace the chromaticity values for first-orderinterference and second-order interference for white polychromaticincident light. The parameter that varies along these curves is theoptical path length as determined in the calibration methods describedabove.

Thus, another aspect of the invention is an embodiment of a method ofusing an electrostatic actuator having a number of control plates forcalibrating an interferometer having first and second reflectingsurfaces and an optical gap between them. Such a method embodimentincludes steps illuminating the interferometer with monochromatic light,controlling the optical gap by selectively applying a fixed voltage toeach control plate, and detecting light reflected from theinterferometer, thereby establishing a calibrated relationship betweenthe applied control-plate voltage and an optical path length of theinterferometer.

Methods for fabricating an interferometer device in accordance with thisinvention, for fabricating arrays of such devices, and for fabricatingan optical interference pixel display including Fabry-Perotinterferometer elements are described in the co-pending and commonlyassigned applications incorporated by reference hereinabove.

INDUSTRIAL APPLICABILITY

Devices made in accordance with the invention and methods performed inaccordance with the invention are useful in calibration forinterferometry and in calibration of devices used for display ofinformation, for example. The devices and methods allow calibration of aFabry-Perot device with a finely divided series of steps in the cavitydistance, without using color filters or color-sensing devices. Thecalibration may be accomplished using a single light source, such as anLED or laser with a substantially single-wavelength emission, and asingle photosensor. Thus, these methods can be used to make anall-digital chip whose interferometer devices may be calibrated usingonly a single wavelength reference. Optical-interference pixel displaysmay be made using a number of the interferometer devices, arranged in anarray, for example. The devices may also be used in otherinterferometric applications.

Although the foregoing has been a description and illustration ofspecific embodiments of the invention, various modifications and changesthereto can be made by persons skilled in the art without departing fromthe scope and spirit of the invention as defined by the followingclaims. For example, actuators including split actuators andintegral-DAC actuators operable by magnetic or piezoelectric or othermeans may be substituted for the electrostatic actuators illustrated anddescribed. Also, optical elements other than the lenses illustrated,such as mirrors, prisms, or holographic optical elements, may be used todirect incident and/or emergent light. In the methods, the order ofsteps may be varied for various applications.

1. A Fabry-Perot interferometer, comprising: a) substantially parallelfirst and second reflecting surfaces spaced apart by an optical gapbetween the first and second reflecting surfaces; and b) means forcontrolling the optical gap, including a plurality of electrostaticcontrol plates, each electrostatic control plate having a fixedcontrol-plate area and each control plate being adapted to control theoptical gap by application of a control-plate voltage, the control-plateareas being related by integral ratios.
 2. The Fabry-Perotinterferometer of claim 1, wherein the integral ratios by whichcontrol-plate areas of the control plates are related are powers of two.3. The Fabry-Perot interferometer of claim 1, wherein the control platesof the plurality of control plates are disposed in a nestedconfiguration.
 4. The Fabry-Perot interferometer of claim 3, wherein theplurality of electrostatic control plates disposed in a nestedconfiguration includes a round innermost control plate, and each controlplate of the plurality of control plates except the round innermostcontrol plate is annular.
 5. The Fabry-Perot interferometer of claim 3,wherein the plurality of electrostatic control plates disposed in anested configuration includes an outermost control plate, and eachcontrol plate except the outermost control plate is surrounded byanother control plate.
 6. An optical interference pixel displaycomprising a plurality of the Fabry-Perot interferometers of claim
 5. 7.An optical interference pixel display comprising a plurality of theFabry-Perot interferometers of claim 1.